The formation of secondary pollutants of O3 needs a photochemical reaction between the primary pollutants of
nitrogen oxide (NOx) and volatile organic compounds (VOCs) combined with ultraviolet sunlight (UVB) [4]. NOx refers
to the molecules of nitrogen dioxide (NO2) and nitric oxide (NO). The primary sources of NOx are emitted from motor
vehicles and combustion processes. Meanwhile, the presence of VOCs are mainly due to industries and high traffic
volume.
According to the Malaysian Department of Environment [5], the perfect combination between the conducive
atmospheric condition and the emission from motor vehicles and industrial activities will result in the formation of O3.
The burning of hydrocarbon fuels from transport, heating from homes, factories and business, manufacturing process and
power plants are the main sources of O3 [6]. O3 was also detected to be highly active from 7 am to 7 pm due to the
presence of sunlight [7].
The other contributors to the formation of O3 are CO and methane (CH4). Both air pollutants of CO and CH4 are emitted from man-made activities such as motor vehicles, landfills, power plant and industries facilities. At times, natural
sources such as, lightning, trees and soil can also contribute to the formation of O3 concentration.
In statistical analysis and air pollution, regression analysis was widely used as a tool to predict the concentrations
level of some air pollutants. This study used several independent variables to form an equation in terms to predict the
level of O3 concentrations and the equation was known as multiple linear regression. The relationship between dependent
variable and independent variables could be concluded in multiple linear regression model with several analyses [8].
However, outlier is one of common issues in developing regression model. Even a single point of outlier could distort
the regression analysis and lead to incorrect inferences [9]. Outlier is a huge different observation point from another
point of observation. In other words, the point of observation which is different to the general trend of the observation
[10]. The presence of outliers will affect the accuracy of the model prediction in the forming of regression coefficients
[11]. Every data cannot be claimed to be free from outliers [12] and most of studies did not take the assessment of outliers
into their prediction consideration. Sometimes the offense in data recording and sampling, the error in data acquisition or data management and the damage of monitoring instrument in data recording are the factors that contribute to the
formation of outliers [13].
According to Yahaya [11] and Field [14], the whole influential outlier from the data observation could be measured
using standardized residual or Cook’s distance because the influential for the overall of outliers depend on the response
variable. The aim of this study to approach M-estimation method from robust regression to minimize the number of
influential outliers from response variable of the next day prediction (D+1) of O3 concentration level in urban area of
Shah Alam.
1.1 Variable Selection
The variables used in this study were consist of ozone (O3, ppb), wind speed (WS, km/h), ambient temperature (T, oC),
dioxide (SO2, ppb) that were chose as the predictors in order to predict the level of O3 concentration level for next day (D+1). The variables are selected [15-24] by the factors that associated with high contribution to the formation of O3
concentration such as the conducive meteorological factor of temperature, wind speed and relative humidity when they
combine with the other air pollutants.
2. Methodology
The purpose of this study is to develop the next day prediction model (D+1) of O3 concentration level for Shah Alam
using robust method by M-estimation in order to minimize the influential outliers from response variable. The procedures
of this study are illustrated in Fig. 1. Before the robust regression model developed, the assessment of the outliers will be conducted to identify the influential outliers from response variable using Cook’s distance and standardized residual.
Thus, M-estimation method will be used to reduce the contamination of the influential outliers from response variable
using tuning constant in developing the prediction model. Tuning constant controls how sharp M-estimation as an outliers
detector that contaminated response variable data. Nine method from M-estimation has been introduced such as Huber,
Andrew, Bisquare, Cauchy, Fair, Talwar, Logistic, Welsch and Hampel. This method will be compared with classical
method of ordinary least square in order to determine a better model to be used in the prediction of O3 concentration level.
2.1 Site Selection
The monitoring station in Shah Alam is located at Taman Tun Dr. Ismail (TTDI) Jaya Primary School (N 3.077324o,
E 101.510323o) nearby a residential area. At the same time, this station is located at the main transportation area such as major road, highways, and airport. Besides, Shah Alam city is located between Petaling Jaya city (east) and Klang town
(west). Shah Alam station is selected due to the highest level of O3 concentration in Malaysia according to the rising
number of registered mobile vehicles in Shah Alam throughout 2003 [25] and commencing on 2003, the increased burning
of industrial waste including from hotels, commercial centres, institutions and night markets tend to produce large
emission of NOx and VOCs which are the main element of O3 formation [26].
Muhamad et al., Internatinal Journal of Integrated Engineering Vol. 12 No. 1 (2020) p. 270-279
272
Fig. 1 - Research flow
2.2 Data Acquisition
In air pollution monitoring procedures, United States Protection Agency (EPA) standardized some guidelines to
measure air pollutants and meteorological variables [27]. The air pollutant and meteorological variables were monitored
by Teledyne Ozone Analyzer Model 400A UV Absorption (O3), Teledyne Model 200A (NO and NO2), Teledyne Model
100A (SO2), Teledyne Model 300 (CO), Met One 010C Sensor (WS), Met One 062 Sensor (T) and Met One 083D Sensor (RH) [28]. The primary data was managed by Alam Sekitar Malaysia Sendirian Berhad (ASMA), which is the private
company under supervision of Department of Environmental Malaysia (DoE). The secondary data from 1st January 2002
until 31st December 2012 were obtained from Department of Environmental Malaysia (DoE).
2.3 Data Management
In this study, the hourly concentrations for each variable selected were transformed into daily 12 hours average
concentration, from 7am to 7pm because the level of O3 concentration level was suspected to be highly active during
morning and evening [29]. According to Mohammed, Ramli, and Yahaya [7], most of the areas have a large emission of
O3 formation factor from morning till evening. This study only used 12 hours average ozone concentrations from 7 am
until 7 pm to predict the next day (from 7 am until 7 pm) ozone concentrations.
Missing values is one of the problems in the process of data acquisition that may lead to the interrupted analysis. The
offence in data recording and sampling, the failure of machine and human error are the several reasons that contributed to the missing values observation [30]. One of the suitable methods in the imputation of missing values for air pollution
data is by using the mean imputation technique as suggested by [31]. The missing values will be replaced by the mean
obtained between the above value and the below value also known as mean above below method (MAB) as followed by
Noor et al. [30]. The data from 2002 until 2012 were randomized into 80% and 20% as suggested by [12] where 80% of
the data were used for training while the other 20% were used for validation.
2.4 Influential Outliers Identification
The influential point of outliers is the case where there is existing larger residual that differs substantially from the
other observations [32]. Influential outliers are any point that has a large effect on the analysis of regression. According
to Sarkar, Midi, and Rana [9], the results of the analysis will lead to incorrect inferences by the unduly influence of outliers. The change of regression coefficients after removing several data observation showed that the data before was
influenced by outliers. This study only considers the influential outliers from response variable by computing standardized
residual and Cook’s distance assessment as shown in Table 1.
Muhamad et al., International Journal of Integrated Engineering Vol. 12 No. 1 (2020) p. 270-279
273
Table 1 - The assessment of the influential outliers from response variable
2.5 M-estimation
Huber [35] introduced M-estimation as the simplest method in the detection of outliers from response variable.
Mestimation is an extension from the maximum likelihood estimation where the main principle in M-estimation is to
minimize the residual function of weighting function and the steps of M-estimation are shown as follows [36] and [37],
• Step 1: Test assumptions of ordinary least square.
• Step 2: Detect the presence of outliers in the data.
• Step 3: Calculate regression coefficient ( ) with ordinary least square.
• Step 4: Calculate initial residual value:
(1)
• Step 5: Calculate initial value of standard deviation:
(2)
• Step 6: Calculate value:
(3)
• Step 7: Calculate the weighted value of Bisquares (Tukey):
(4)
• Step 8: Calculate using weighted least square method with weighted .
At the first step, each of the regression model for O3 (D+1, D+2 and D+3) was checked to ensure the test assumptions
in ordinary least square (OLS) were satisfied. The presence of the outliers were detected using standardized residual and
Cook’s distance at step two. Then, the regression coefficient was calculated to obtain the predicted value ( ) for O3
using the method of OLS estimate. In order to obtain regression coefficients from Mestimation, the estimator for
standard deviation that we denoted as sigma is rescaled to median absolute deviation (MAD) by the factor 1.4826 at
step 5, where 1.4826 is the value when the residual is normally distributed and the sample is large.
From step 6, the proportion of the residual from the estimated scale of standard deviation ( ) was obtained to be used
in the Bisquare weighting function (step 7) where 4.685 represents the value of tuning constant of Bisquare at 95% level
of efficiency. Step 4 until 7 were repeated until the value of regression coefficient in step 8 converged. The same
steps were applied in other weighting function (Huber, Andrew, Cauchy, Fair, Talwar, Logistic, Welsch and Hampel) to
obtain the value of regression. Table 2 shows all weighting function used in M-estimation.
2.6 Performance Indicator
Performance indicators are used to evaluate the performance and the adequacy of the models. The performance
indicators (Table 3) are consists of normalized absolute error (NAE), Root Mean Square Error (RMSE), Index of
Agreement (IA) and prediction accuracy (PA). The best prediction model will be obtained by comparing the performance
indicators between the models.
Muhamad et al., Internatinal Journal of Integrated Engineering Vol. 12 No. 1 (2020) p. 270-279
274
Table 2 - Weighting function of M-estimation [38]
Note: ψ ( ) = ρ’ , = residual and a, b, c = tuning constant.
Muhamad et al., International Journal of Integrated Engineering Vol. 12 No. 1 (2020) p. 270-279
275
Table 3 - Performance indicator (PI) [39]
Note: N = Number of sample daily measurement of a selected sites, = Predicted value of one set daily data,
= Observed values of one set daily data, = Mean of the predicted values of one set daily data
= Mean of the observed values of one set daily data
3. Results and Discussion
3.1 Air Pollutants Characteristics
Shah Alam was located at a busy main transportation area and thus exposed to traffic congestion. Almost daily sees
Shah Alam polluted by 32.421 ppb of O3 concentration. The reading of O3 concentration was very high on 15th March
2003 at 97.00 ppb. This is due to the rising number of registered mobile vehicles in Shah Alam throughout 2003 [25],
and that same year saw the increased burning of industrial waste including from hotels, commercial centres, institutions
and night markets [26]. Table 4 summarizes the characteristics of O3 concentrations level for Shah Alam.
Table 4 - Summarizes the characteristics of O3 concentrations level for Shah Alam
Shah Alam O3
Mean 32.421
Median 31.250
Mode 32.421
Standard Deviation 11.441
Variance 130.907
Skewness 0.657
Kurtosis 1.030
Maximum 97.000
Percentiles 95% 52.750
Percentiles 99% 65.709
Following up to these scenes, the formation of O3 become active due to the high presence of NOx (108.330 ppb), CO
(6214.167 ppb) and VOCs from the vehicles and industrial burning respectively. The measurement of dispersion showed
that the level of O3 concentrations for Shah Alam is moderately skewed when the skewness value is 0.657) and this tended
to have a standard deviation with value 11.441. Besides, the distribution for O3 concentrations has a positive kurtosis
with value 1.030.
The percentage of outliers for O3 in Shah Alam was described using box and whisker plot. The points that were out
of the box and whisker plot indicated that the observation of the outliers. The percentage of outliers suspected for Shah
Alam and is 1.69 as shown in Fig. 2.
Muhamad et al., Internatinal Journal of Integrated Engineering Vol. 12 No. 1 (2020) p. 270-279
276
Fig. 2 - Box and Whisker plot for O3 concentration level
3.2 Ordinary Least Square
Since all of the assumption of ordinary least square estimate have been fulfilled, thus the multiple linear regression
model for next day (D+1) prediction has been developed as show in Table 4. The multiple linear regression model in
Table 5 are evaluated by performance indicators. The average error is 5.488 and the average accuracy is 0.5127.
Meanwhile, the model show that 20.56% of the total variation in O3, D+1 is explained by the regression line using the
predictors.
Table 5 - Multiple linear regression model and performance indicator
The influential outliers from response variable was identifed at 172 observation after compute the assessment of
standardized residual and Cook’s distance. Furthermore, the influence of the outliers from response variable could be
illustrated using scatter plot of Cook’s distance against centered leverage value. The point of observation that was above
the line indicates the observation of influential outliers from y-direction after conducting the assessment of standardized
residual and Cook’s distance. After removing the outliers from response variable, the uncontaminated data from response
variable is remained below the horizontal line of Cook’s as in Fig. 3.
Fig. 3 - Box and Whisker plot for O3 concentration level
( a) The influential outliers from respo nse
variable ( b) After remove the influential outliers from response
variable
Muhamad et al., International Journal of Integrated Engineering Vol. 12 No. 1 (2020) p. 270-279
277
3.4 M-Estimation Models
The models developed by M-estimation use tuning constant to detect the outliers from response variable. Tuning
constant is located in the weighting function of Huber, Andrew, Bisquare, Cauchy, Fair, Logistic, Talwar, Welsch and
Hampel. The tuning constant has an important role in determining the regression coefficient in order to develop the model
in the prediction of O3 concentrations level for next day (D+1). Table 6 shows the models developed to predict the level
of O3 concentrations in Shah Alam using the nine M-estimation methods. Then, each next day (D+1) prediction model of O3 concentrations level from M-estimation was evaluated using
performance indicators. The lower error (NAE and RMSE) and the higher accuracy (IA and PA) indicated that the model
is appropriate. In order to determine a good model among these nine methods, the ranking method of performance indicators [40] was conducted where the error of NAE value and RMSE value are ranked in increasing order (1 = the
smallest value of error to 9 = the largest value of error) and the accuracy of IA value and PA value are ranked in decreasing
order (1 = the largest value of accuracy to 9 = the smallest value of accuracy). Hence, a good Mestimation method was
found by the smallest summation from ranking the performance indicators of each method as shown in Table 7. The ranking with the smallest summation (Table 8) which is the Fair method is seen as a good M-estimation model
to predict the level of O3 concentrations in Shah Alam for next day (D+1). The comparison of the result between
Mestimation (Fair) and ordinary least square method was shown in Table 9.
Table 6 - Robust regression model by m-estimation for Shah Alam next day prediction (D+1)
